My own preference is that the stem isn't shiny from any kind of oil or wax which feels slippery, and rubs off. I want the stem itself to shine like a mirror once the oxidation is gone. Once I get the stem to the point you've mentioned (which comes from a multi-grit wet-sanding process...after the oxidation was dealt with either with Oxyclean or bleach/water soak), the shining itself comes from a very quick buffing process. I have a bench buffer with dedicated wheels for different compounds. Tripoli, followed by white diamond, followed by either jewelers rouge (that's the Ed James method), or a j.r. equivalent - Simichrome polishing compound. The result is a mirror-like finish.
However, I've used most of the methods shared, and echo much of what's said above. Not everyone has these tools, and not everyone wants them. Many methods work just great (as evidenced above), this is just one more.